NEHRP Provisions allow base overturning moment to be reduced by 25% at the soilfoundation interface For a moment frame, the column vertical loads are the resultants of base overturning moment, whereas column moments are resultants of story shear Thus, use 75% of seismic vertical reactions

Moments and shears for reinforcement should be checked for the overturning case Plastic soil stress gives upper bound on moments and shears in concrete Horizontal equilibrium: Hmax< φµ(P+W) in this case friction exceeds demand; passive could also be used

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 24

Results for all Seismic Resistant System Footings Middle: 5'x30'x4'-0"

The subtitles are effectively a table of contents, although the topics are not really treated in that specific order. This unit is primarily aimed at the structural engineering of foundations, not at the geotechnical engineering. This presentation relates to example computations in Chapter 5 of the FEMA P752, NEHRP Recommended Provisions: Design Examples.

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First model: soil pressures in unmoving soil caused by force at top of deep pile; most of stress resisted at top of pile; only small stresses below about twice the characteristic length of pile. Second model: unloaded pile subject to earthquake ground motion; small stresses induced by upper levels of soil lagging behind deep motion. Note opposing directions of “push”. Third model: both types of force act on pile. The lag of structure induces inertial forces at top of pile similar to static force in first model; net force shape similar to static situation.

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As building lags behind ground motion, induced inertial forces must be transferred between footing and soil. Design may consider that inertial forces are transferred as passive earth pressure on face of footing, friction on bottom of footing, or both.

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Same single story structure; now on deep pile foundation. One leg shows pile displacements; other shows resulting earth pressures; third diagram shows bending moment in pile. One reference that has long been used for laterally loaded piles is the Navy Design Manual 7.2, Foundations and Earth Structures. However, it and most other older methods are based upon assumptions of linear behavior in soil. Over the past two decades considerable progress has been made in developing design tools rooted in the strongly nonlinear behavior of soil. “LPILE” is one widely used example that allows the user to specify soil parameters that model resistance of soil to lateral movement of piles.

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As aspect ratio of building height to width increases, overturning moment becomes significant; induced vertical forces must be transferred in addition to horizontal pressures. (Similar vertical forces in footing result from column moments not specifically related to overturning.) Slide shows overturning moment being resisted below basement of medium sized building; horizontal pressures are transferred at the basement walls.

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This example of tall building with shear wall continuing through deep basement shows that the horizontal and vertical forces can be resisted by different portions of foundation structure. Basement wall resists horizontal forces near ground surface; vertical forces resisted by piles at base of wall.

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Reinforced concrete footings are proportioned according the provisions of ACI 318, Building Code Requirements for Structural Concrete. It is often opined that foundations should not yield, due to the high cost of foundation repair. However, nonlinear soil behavior is common in strong ground shaking, and it is traditional to design foundations for the reduced forces computed with the response modification factor, R, used for the superstructure. Neither the NEHRP Recommended Provisions nor earlier model building codes required the use of amplified forces for foundation design.

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ASCE 41 has a good discussion of the plastic behavior of soil beneath eccentrically loaded footings. Just as for analysis of structural members, plastic analysis of a footing is simple “by hand”, but not so with a computer. Both uplift and nonlinear behavior introduce complications in conventional analysis. Many commercially available software packages for structural analysis now handle the uplift case; a smaller set can also handle nonlinear behavior.

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Title slide for 7-story building showing plan of steel building.

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The gravity load allowables are set to control settlements. The values between 20 and 40 feet should be interpolated. The bearing capacity is the classic value from theoretical soil mechanics (normal gravity loads are checked). The subject of strength design in soils is in its infancy, and many geotechnical professionals are not yet comfortable with strength design concepts. Note that the term phi is Resistance Factor for bearing capacity. B is the footing width.

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The size of the square footing is controlled by the allowable bearing pressure at total loads, and the thickness is controlled by two-way shear at the critical section (“punching shear”). The point of this information is primarily for later comparison with footings designed for seismic loads.

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The only portion of the steel frame that resists lateral forces is at the perimeter, thus, the only footings that will be affected by the seismic load are at the perimeter.

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The image is taken from the RAM Frame analysis used to design the steel moment resisting frame for seismic loads.

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Load combinations for strength-based design, which is the fundamental method for earthquake resistant design. Greek rho is the redundancy factor. Q is the effect of horizontal seismic motions. The 0.2SdsD is an approximation for the effect of vertical earthquake motions. For the footings, the horizontal motions produce vertical and horizontal forces, as well as bending moments, at the base of each column. Dead and Live loads are taken to produce only vertical forces in this example.

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Grid A-6 is at the lower left corner of the plan, and A-5 is adjacent. (Go back three slides to show the location on the plan.) Recall that the seismic reactions can be positive or negative; what is given here is for motion in the positive x and y directions. Carefully note that subscripts x and y on the load effect E refer to the global north-south and east-west, respectively, but the subscripts x and y on the moments at the column bases refer to the local strong and weak axes, respectively, which is just the opposite as the global directions, unfortunately. The most significant point of this slide is that seismic uplift at A-6 exceeds the dead load by a considerable margin. It is possible to place a footing with sufficient size to resist the uplift and the overturning moment, but it is much more economical to combine one footing for the two locations. These reactions include the effects of horizontal torsion on the system. Also recall that the footing must resist horizontal forces.

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The Provisions allow an overturning moment reduction of 25% at the soil-foundation interface.

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None of these loads include the weight of the footing. P is positive in compression. M is positive by the local right hand rule. This is not the maximum downward load; it is the maximum ratio of moment to axial load for the additive combos.

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Note that the net vertical load is upward without the weight of the footing. It so happens that this combo also gives the maximum eccentricity, when combined with the weight of footing and soil.

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Slide is drawn for the case with substantial moment, such that uplift will occur at the heel. Note that eccentricity e changes as W changes. For our footing, L will exceed 25 feet by some margin, given that the two columns are 25 feet apart.

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Initial approximation of W is simply to keep the resultant of earth pressure within the footing. It must be somewhat larger in order to control the bearing pressures. Note that the load factor on W does not include the amplifier for vertical seismic acceleration; this is the author’s interpretation of the NEHRP Provisions. The minimum B used to find the nominal bearing capacity is found by comparing the width of the footing and the half length of the loaded area. The half length is used because the soil pressure is not uniform.

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Slide shows basis of plastic design of foundation.

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Note how much larger the footing must be for the counteracting case. Also, it would have been even larger if the elastic solution were used in lieu of the plastic solution.

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Notes for additional checks for foundation design.

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Given the combined footing strategy, footing sizes are more strongly influenced by the uplift on columns at the ends of frames than by the moments transmitted by the columns. Note that a complete perimeter grade beam would be a very feasible solution for this project, especially in cold climates where a continuous perimeter wall for frost control is necessary. A 4 ft by 4 ft continuous grade beam would be sufficient.

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The screen capture is from the RAM Frame analysis of the structure, and the small plan is based on the same grids used for the 7 story moment frame. The braced frames appear to be 8 stories high, because there is a small penthouse over the core.

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The fundamental method is the same as used in the previous example: Determine the total applied vertical and horizontal loads and the moments. The complicating factor here is that the bending is significant about two axes simultaneously. Elastic solutions can be found from software that has the capacity for compression-only springs; SAP2000 was used in this case. Plastic solutions typically need to be done “by hand,” although spreadsheets are a great asset for the successive trial nature of the solution.

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Slide shows the results from “hand” analysis for plastic distribution and for SAP2000 elastic solution. See Chapter 5 of FEMA P-751 for more detail on the solution, as well as the design of the footing cross section for moment and shear.

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Title slide for pier foundations.

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Most pile analysis for lateral loads is performed assuming linear response in the pile itself, although it is now common to consider nonlinear soil response. Some “byhand” plastic techniques do make use of the classic pile stiffness idealizations.

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Note the logarithmic scale on the vertical axis.

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This passive pressure mobilization is useful for inclusion of the pile cap. It is from ASCE 41. Delta/H is the imposed displacement as a fraction of the minimum dimension of the face being pushed into the soil mass.

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Plots of group effect factors computed based on Rollins et al., “Pile Spacing Effects on Lateral Pile Group Behavior: Analysis,” Journal of Geotechnical and Geoenvironmental Engineering, October 2006. The plot shows four curves, each for a different spacing (in terms of pile diameter). The horizontal axis is the number of rows of piles, and the vertical axis is the Group Effect Factor.

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Note that the shear forces in the pile (as well as deformations and bending moments) carries to greater depths in soft soils than in firm soils. Pile (or pier) foundations are often used in stiff soils to control settlement of heavy structures or heave of expansive soils.

The drawing shows one of the piles with detail of reinforcement. “D” is pile diameter. See Chapter 5 of FEMA P-751.

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Additional considerations for Pile Foundations. The equation is from ASCE 7-10 Section 12.13.5.2, where F is the design tension/compression force in the foundation tie beam and PG is the load in the pile.

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Required iin higher seismic design categories for softer soils. It is designed for “pure” axial force. Fundamental objective is to prevent relative lateral displacement between column bases. It “fixes” the column bases for translation, but it is not intended to restrain rotation at the column bases.

NEHRP Provisions allow base overturning moment to be reduced by 25% at the soilfoundation interface For a moment frame, the column vertical loads are the resultants of base overturning moment, whereas column moments are resultants of story shear Thus, use 75% of seismic vertical reactions

Moments and shears for reinforcement should be checked for the overturning case Plastic soil stress gives upper bound on moments and shears in concrete Horizontal equilibrium: Hmax< (P+W) in this case friction exceeds demand; passive could also be used

Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

Foundation Design - 24

8

Instructional Material Complementing FEMA P-751, Design Examples

Results for all Seismic Resistant System Footings Middle: 5'x30'x4'-0"